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Studies in DistillationDesign of Rectifying Columns for Natural and Refinery Gasolirw

by.K. LEITIS .4KD G. L. hfATHESONDepartment of Chemical Engineering, Massachusetts Institute of Technology. Cambridge, Mas>.

T he Hausbrand equations fo r binary mixture s are applied to the solution of problems ir c con-details of which are illustrated by a specijic problemtinuous rectification of natural gasoline. S teps of the compu tation are outlined, the

HE design of rectifying equipment for natural andrefinery gases is complicated by the presence in theT ixtures of a large num ber of components. Th eproblem can be solved by applying the ordinary H ausbrandequations for binary m ixtures successively to all of the com-ponents whose propelties influence the separation. How-ever, the multip licity of th e operations of com puta tion issufficient to confuse one unfamiliar with the technic of han-dling the equations. Because of the growing imp ortan ceof rectification in the industry, it seems worth while to out-line and illustrate the steps to be taken in solving a prob-lem of this sort.The following nomenclature will be employed :V = moles of vapor rising from any plate per unit time0 = moles of overflow descending from any plate per unit timez = mole fraction in liquid phase of any particular componenty = mole fraction in v apor phaPe of any such componentF = moles of feed t o the column per unit timeD = moles of final product (distillate), whether vapor or liquid,W = moles of reqidue leaving bottom of apparatus per unitP = vapor pressure of component under consideration in pureT = total pressure on appar atusp = partial pressure of component under consideration

under consideration

leaving appar atus per unit timetimestate a t temperature in question

Count the plates up from the feed plate toward the topand down toward the bot tom. Call any particular plateabove the feed plate the nth plate and below, mth. Cal lthe top plate the pth an d the bottom plate-i. e., the still-the wth plate. Designate the conditions referred to bymeans of a subscript indicating the location of the materialin question or the point from which the material came.Thus , y,, is the composition (mole/fraction of the com-ponen t in question) of th e vapor rising from the n th plate,xf is the composition of th e feed to the colum n, etc .Assuming contin uous ope ratio n of such a rectifying colu mn,Hausbrand equated input to output of a given componentin a section of the a ppa ratus above the n th plate, as follows:

y,V, = T n + i O n + i f X d DThe left-hand side of the equ ation is the total am oun t ofcomponent entering the top of the column from the nthplate per un it time, while the first term of the right-handside is the a mo unt of thi s com ponent flowing in the overflowfrom the top of the column down on the nth plate , and thesecond term is the am ount in the dis t i lla te . Hausbrandemployed weight units, but for reasons which will appearpresently it is more convenient in this particular case to usemoles. Th e expression X d D is determined by the condi-tions of the problem, and the amount of vapor and over-flow can be calculated a t an y temper ature level from a heatbalance. I n recent years it has become commo n practicein the case of bin ary mixtures to tak e adv antag e of th e fact

that the molal heat of vaporization of the componeiits i sreasonably constant under ordinary conditions of rectifica-tion by assuming average constant values for Vn n d On+above the feed plate and for the corresponding values ofV , an d 0, - below it, thus making it possible to use thegraphical stepwise metho ds of design which have so generallyreplaced the former algebraic technic.I n using the above equation, Hausbrand calculated thevapor composition, y from the liquid composition on theplate above, and then determined the liquid composition,xn, y the use of the equilibrium diagram, thus proceedingdown the column. I n the case of natu ral gasoline the proc-ess can be simplified because of the fact that the componentsof th e mixture follow Rao ult 's law, at least within th e ac-curacy of design. Thus, assuming 100 per cent plate ef-ficiency, the partial pressure of any particular componentabove the n th plate is equal to XZ,,nd this in tu rn is identi -cal with its partial pressure in th e vap or above tJhe plate,yn7r. Hence,

Y" = znP,/n,and consequent ly one may rewrite the Hausbrand equat ion as

Similarly, below the feed plate,

It should he clear that by means of these equations one cancompute the change in concentrat ion from plate to p late ina n y p a r t of the column, once the conditions on any givenplate are known.C H A R A C T E I ~ I S T I CR O B L E MN DESIGN

It will be worth while t o consider a characteristic prob-lem in design. One will know the Composition and am ou ntof the feed to the column; the temperature and pressureunder which it exists; the tem perature which it is practicableto maintain in the reflux condenser a t the top of the columnwith the cooling means available; the point a t which it isdesired to effect the separat ion; and the allowable o v e r l a pi. e., the amount of high-boiling material which may betolerated in the overhead distillate and of low-boiling ma-terial in the residue from the still at the bottom of the column.With these da ta a t hand, the following steps of co mpu ta-tion are necessary:

Calculate the amount and exact composition o f the die-tillate and residue.Determine the pressure which must be maintained on thecondenser in order to produce the reflux which is necessary forthe functioning of the column. This is the operating pressure.8, of the apparatus.

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May, 1932 I N D U S T R A L A S D E N G I N E E R I N G C H E A I I S T R Y 195(3) Assuming for the mo men t a suitable va lue of t he reflux,0 , o the top of the column from the reflux condenser, calculatethe com position of th e reflux. Th is will, of c ourse, depend onthe type a nd method of operation of the condenser employed.(4) Calculate th e composition of th e vapor from the topplate, and, from this, that of the liquid on the top plate and itstemperature.( 5 ) Calculate th e tempe rature of t he still and the compositionof the vapors rising from it.(6) . From a heat balance on the column, determine th e varia-tion in the reflux through the column. One can immediatelydetermine by such a balance the reflux from the bottom of t hecolumn to the still, and it is usually sufficiently accurate towsum e the change in reflux per degree of t emp eratu re rise upthe column constant, except a t the feed plate where the reflux isincreased by th e amoun t of liquid in the feed.By use of the Hausbrand equation applied from plate toplate calculate the concentrations and temperatures on theplates, working down from the top and up from the bottom.Tnspection of the results of the preceding operations asthe temp eratures of t he plates app roach each other towards th emiddle of t he column will enable one to judge with reasonableprecision wheth er th e amou nt of reflux assumed for the operationof the column is satisfactory. If not, read just it to a satisfactoryvalue and rep eat steps 3 to 6, inclusive.By study of the compositions determined by working upfrom the bottom, pick a suitable feed plate. Estimate the

concentration on t h s plate of th at com ponent of highest boilingpoint which does not a ppea r in the residue in appreciable amou nt.If necessary, recalculate the composition on the plate below andcorrect fo r th e concentra tion of t,his com ponen t on it. Thenproceed with the co mp utatio n of th e concentrations up thecolumn until the concen tration of th e lowest-boiling const ituen tof the residue which does not appear in appreciable amount inthe distillate has become negligible. If the concentrations thusdetermined correspond substantially with those calculated bystarting down the column from the top, the problem is solved.If not, the concentration on the feed plate must be reeatimated,and this last operation repeated. The number of plates thusdetermined, corrected for the plate efficiency, gives the numberof plates required in the column when operated under these con-ditions.(IO) To determine t,he influence of reflux ratio in column sizeand heat consumption, these operations must be repeated for anumber of different values of reflux. The plotted results willmake it easy to determine the best operating conditions.

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ILLUS'FRATIOX O F DETAILS F PROBLEMTh e detail of these ste ps will be best u nderstood from aspecific illustratio n. Assume as a feed stock a materialcontaining 26 mole per cent of methane and permanentgases, 9 per cent ethane, 25 per cent propane, 17 per centbutane, 11 per cent pentane, and 12 per cent of hexane andhigher. Assume th at the am oun t of isomers of th e normalhydrocarbons ma y be neglected an d th at t he hexane andhigher hydrocarbons average heptane. Assume that con-dit ions are such that one can maintain an effective toptemperature-i. e., a tempe rature of th e gas an d reflux,within the condenser itself , of 70 " F. (294" K.) . The feedis pumped in at 100" F. (311" K.). It is desired to take allpropane and l ighter overhead, and al l butane and heavieras residue, but it is allowable to have 1 per cent of butanein the overhead distillate and 0.1 per cent propane in theresidue. Th e reflux condense r is of a typ e in which th ev ap o r s ~ravel with th e l iquid through th e condenser and areseparated af ter having been brought to the f inal condensertemperature of 70 " F. Consequently, the final gas is inequilibrium with the reflux liquid.

Were the separat ion complete, there would be60 moles of distillate a nd 4 0 of residue for each 100 molesof feed. Consequently, in the act ual column the buta neIn the distillate will be approximately 0.6 mole and thepropane in the residue 0.04. On th e basis of this, the follow-ing table, showing the distribu tion of th e comp onents of 100moles of feed between distillate and residue, should be self-explanatory:

STEP1.

HYDROCARBOS D I S T I L L ~T E R E S I D C EM o l e s M o l e yo Moles .Vo le %

CH I+ 2 6 . 0 4 2 . 9 . . . . . .CzHe 9 . 0 1 4 .9 . . .C3H8 24.96 41 .2 0. 04 0 : 1CIHK 0 . 6 1 1 . 0 1 6 . 3 9 41 . 6CSHIP . . . . . . 11.0 2 7 . 9CEHl4+ ~ . . . . . . 12.0 3 0 . 4

Total 6 0 . 5 7 100.0 3 9 , 4 3 1 0 0 . 0~ __

STEP2. At the temperature of the condenser the pres-sure must Le such that the overhead ga.j or distillate is atits dew point, since it was separate d from a liquid condensedfrom it by cooling at constan t pressure. Therefore, th e par-tial pressure of each com ponent in th e gas must of necessityequal the par t ial pressure of that same component in theliquid from which th e gas was last separated, a nd w ith whichit was in equilibrium. Kow at the effective condensertemperature, 294" K ., the pressure of pure e tha ne is 38atmospheres, of propane 8.8, an d of buta ne 2.2. Conse-quently, one can write the following equations:pz = 3822 = 0 . 1 4 9 ~p , = 8 . 8 ~ 3= 0 . 4 1 2 ~pa = 2.224 = 0.01T

Furthermore, neglecting the solubility of methane and per-manent gases in the liquid, the sum of the mole fractionsm us t obvio usly be unity-i. e., x~ + x3 + z4 = 1. Solvingthese equations, one obtains s = 18.1 atmospheres, whichis the necessary operating pressure on the condenser, andwhich, neglecting pressure drop through the colunin, is thepressure throughout the apparatu s. From the above calcu-lations, 100 x2 = 7.1 mole per cent ethane in the liquid con-densate, 100 z3= 84.7 per cent propane, and 100 x4 = 8. 2per cent butane.Since, f rom the condenser on this equipment,the final overhead gas leaves in equilibrium with the totalcondensate, the figures just given also represent the compo-sition of the reflux to the column.STEP 4. Assume a reflux equal to double the am ou nt ofoverhead vapor . On the basis of 100 moles of distillate,there will therefore be 200 moles of reflux. Co nseq uen tly,the vapor r is ing into the par t ial condenser f rom the topplate will have t he composition show n by th e following table :

STEP3.

Total mo l es ?&CHI = 4 2 . 9C?.Ho = 1 4 . 9 + 1 4 . 2 =CSHO= 4 1 . 2 + 169.4 =CiHio = 1 . 0 + 1 6 . 4 =4 2 . 92 9 . 1210.617.4

1 4 . 39 . 77 0 . 25 . 8-00.0 100.0

Since this vapor must be in equil ibr ium with the l iquidon the top plate, one can write the following equations:1 = 320' K

P 7P z = 0.097 (18 .1) = 1.755 = zzPz 64 0.027P3 = 0 . 7 0 2 ( 1 8 . 1 ) = 1 2 . 7 = Zap3 17 0.747

1 ,000PI = 0 . 0 5 8 ( 1 8 . 1 ) = 1 . 0 5 = zip, 4 . 6 5 0.226

These equations cannot be solved directly because theycontain six unknowns for three equations, although thereis the four th relationship, Zx = 1. However, the values ofPz, a ,an d P4 are determined by the unknown temperatureof the top plate. This temperature mu st be such th at i twill satisfy th e above relation. It can easily be determinedby successive approximation. As a mat ter of fact, in th iscase the top-plate temperature is 320" K., a t which tem-perature the pressure of each pure com ponent a nd th e corre-sponding mole f ract ion in th e l iquid phase o n the t op plateare shown in the two columns following the equation. Itwill be found that at no other temperature wil l the equa-tions be satisfied. While solution by successive approxi-mation is always in a certain sense unsatisfactory, in the

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I N D U S T R A L A N D E N G I N E E R N G C H E M I S T R I' VOI. 24, NO. 5case of equa tion s of this typ e a little experience soon m akesit easy.STEP5 . The composition of the boiling liquid in t he stillis known. Furtherm ore, i t is boiling under a pressure of18.1 atmospheres. Consequently, the temperature of the

FIGURE . CONCENTRATIONRADIENTHROUGH CoLu>rNstill must be determined by successive approximation as inthe preceding case, and Zy must. equal unity. Th e technicis shown in the following table:

t = 413.5' K.% P P Y (as % )CaHs 0.1 80 0.08 0.44C4HlO 41.6 32.2 13,39 74.06CaHiz 27.9 13.3 3.71 20,52

18.08 100.00CBHl4' 30.4 2 . 9 5 0.90 4.98- -

The composition of the vapor from the still is given in thefifth column .STEP . It is first necessary to determine the conditionin which the feed enters the column. This calculation ismost easily made by reference to the following equation,derived from Raoult 's law an d a materia l balance. CallN the total moles of feed which enter in the liquid state per100 moles of tota l feed, th e tota l moles of a given com-pon ent per 100 moles of feed, an d n the moles of the com-ponent entering in the liquid in the feed. Equ ality of in -put and output givesn o = ' + ; ( + ) 100 -

nThe equation is applied successively to each component andthe condition imposed that Z n = N . At the feed tem-perature, 311" K., the pressure of ethane is 53 atmospheres,'of propane 13.7, buta ne 3.7, pentane 1.05, an d heptane 0.11.Solving these equations, N equals 55.2. In other words,the feed enters this column as 55.2 per cent liquid and therest gas.

1 This temperature IS above the crltical point of ethane . However, forthe purpose of romputing th e small amount of ethan e which wlll dlssolvein th e liquid under theae conditions, in the absence of exact data as t o thesolubility, it is allowable to extrapolate the vapor pressure curve to thetemperature i n question. The figure is rough but undoubtedly sufficientlyaccurate for the purpose In hand

When one endeavors t o make a hea t balance o n this columnto determine the reflux a t the bottom, one finds that the dataavailable on hea t of vaporiz ation a t these high pressures (1 )are unsatisfactory, particularly in the case of th e high-boilingconstituents (i. e., the liquid boiling in the still) . Csingthe highest values which the available data would indicateas possible, the overflow decreases somewhat as one goesdown the column. Using lower values gives an oppositeresult. I n order to eliminate confusing complications, itwill therefore be assum ed th at, in th e case of t his column,the change in the overf low and consequently in the vaporrising up the column is negligible from plate to plate excepta t the feed plate. Hen ce, on the basis of 100 pa rts of feed,the overflow in the upper part of the column is 2 (60.57) =121.1, and the vapor, 3 (60.57) = 181.7. Th e correspond-ing values below the feed plate are 176.3 and 136.9.The Hausbrand equation of the operating lineabove the feed plate isSTEP 7.

However, in this equation the term P , is unknown becauseone does not know th e tempe rature of the p late below.This must be assumed, the value of P read off for each com-ponent, the corresponding values of z computed , and theprocess repeated until a value of t is found which makes22 = 1.

1 = 331' K. P 2Pmz = 12.OGzn+i + 0.899 = 1.23Pax3 = 12.06xn+i + 2.485 = 11.52Pmr = 12,06xn+i+ 0.0603 = 2.79 90 0.01421.5 0.5366.2 0.450-,000

Th e composition of th e liquid on the second pla te down isgiven in the last column. By repetition of this process,using the same equations but with the proper values of Pand xn + 1, one can go down the column from plate to plateThe Hausbrand equation below the feed plate isPT

TO,-, = zm- zul = 0.0429xmP, + 0 . 2 2 3 7 ~ ,Since the temperature of the still is known, the correspond-ing values of P are determined, and one can calculate thecomposition of the overflow from the plat e above directlyas shown by the equations in the following table. Th earithmetical accuracy of the operation is checked by thesumm ation of the concentrations to unity . However, be-fore one can proceed further up the column, it is necessaryto know the temperature of the plate above. This mustbe such that the pressure will be 18.1 atmospheres. It isdetermined by successive approximation as before, as shownin the last two colum ns of th e table:f = 395' K.

Z p P a2 3 = 0.0429zmPm + 0,000224 = 0.00365 62 0.2324 = 0.0429zmPm + 0,093 0,6680 23.5 15.6325 - 0.0429zmPm + 0,0624 0.2214 9.25 2.042 7 I 0.0429zmPm + 0,068 = 0.1066 1.9 0.20

~ -18.1.99965One can proceed from plate to plate up the column by re-peating this s tep.Working down the column from the top andup the column from the bottom in this way, one f inds thatthe propane and butane concentrat ions come together quiterapidly. In other words, the reflux assumed is adequate.If a reflux ratio of one be assumed in this case, it is foundthat the concentrat ion and temperature changes f rom plateto plate through the column are far less and are too smallfor satisfactory operation. In other words, a reflux ratio

STEP 8.

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May, 1932 I N D U S T R I A L A N D E N G I N E E R I N G C H E RI I S T R Y 497of 1:1 is too small . Exac tly what rat io to use must bedecided by th e engineer on the basis of th is type of compu-tation , interpreted in the light of th e operating conditionsin question.STEP . Th e conditions of t he various plates in the columnthus com puted are given in Figure 1. It will be noted thatfour plates below the top plate the propane has fallen to13.9 mole per cent, n-hile five plates above the still it hasr isen to substantially th e same value. In other words,this fifth plate abov e th e still ma y well be chosen as the feedplate. If, however, it is desired to introduce the feed onplates above or below this point, this may be tried out bythe methods now to be discussed.ALLOWAKCES OR HIGH- AKD LOW-BOILINGIATERTALS

The difficulty with the computations so far conductedlies in the fact that they take no cognizance of pentane orheavier above the feed plate, or ethane below the feed plate.There is a certain amount of high-boiling constituents inthe overhead product . Ha d this been exactly known, i tcould have been allowed for in the computations, and theamo unt of these consti tuents in th e upper par t of t he columncomputed. Similar ly , had the exact dat a on th e trace ofethane in th e residue f rom the s t i l l been known, i ts amo untup the column could have been calculated. Fur thermore,the com position of t he liquid on the feed plate a s determinedby these two computation operations-i. e., from the topdown and f rom the bottom up-would be th e same. How-ever , the analytical methods are incapable of determiiiingwith precision these traces of the lowest-boiling, materialsin the s t i ll product and th e highest-boil ing in t he overheadeven in the case of a n operating unit. Still less is the de-signer in a position to predict these in advanc e. However.t o design the unit with assurance, al lowance must be madefor these factors.Theoretically, one could make this allowance by assumingthe amount of these contaminating traces and checkingup by tr ial and error on the column calculat ions unti l thecompositions on the feed plate come together. Th e follow-ing is a practical method of making suitable allowance forthese corrections. Th e percentage of ethan e o n the feedplate m us t necessarily be less tha n t he percentage of thiqcomponent on th e plate immediately above the feed. How-ever , assume, for the moment, th at these concentrat ionsdiffer by a negligible am ount and apply the Hau sbrand equa-t ion for ethane over the feed,

. c qL + l 0.083~J'~- 0.0745The tem perature of th e feed is 363" IC., a t which 1' (extrapo-lated) is 125 atmospheres. Using this value and the assump-t ion tha t z,,+~ = xn, i t is seen that the concentrat ion ofethane on t he feed plate m ust be a t least 0.00795. As willappear later , i t mu st actually be higher than this by a smallam o u n t .Below the feed plate the operating equation for ethaneisz,- , = 0 .0 4 29 ~ 2 , . B y means of thi s , one can r ead ilydetermine the ethane concentrat ion. Thus, on the platebelow the feed, the concentration is about 0.0015. On thenext plate below it would be 0.0003. It is obvious thatquanti t ies as small as this may be neglected. Now usingany desired assumed value for the ethane concentrat ion onthe feed plate, remembering th at this value mu st be some-what bu t no t much above 0.008, one can calculate concen-trat ions up the column from the feed plate by using theHausbrand operat ing equation for condit ions above t he feedalready employed above. Doing this , one f inds th at theconcentration of pentane and heavier above the feed fades

away rapidly and conditions then approximate those coni-puted by figuring down from the top.If one assumes a wrong value of ethane on the feed plate,difficulties are encountered. Thu s, if th e value is too small,the equations will indicate a negative incrpment in ethaneconcentrat ions going up the column a t some plate, usuallythe feed plate or the one above i t . Larger assumed valueswill avoid this difficulty, bu t, unless they are. correct, willindicate on the upper plates where the concentrations ofpentane and higher have fallen to a negligible point-ratiosof eth ane :pro pan e:b uta ne which are out of line with thosecomputed by working down the column and which, there-fore, are incompatible with the column set-up. Thus, bysuccessive approuimation, one can determine the properethane concentration on the feed plate.

P L A T E NUMBER FROM TOP O F C O L U M N4 2

40

Lz36

34

32P L A T E NUMBER F R O M B O T T O M OF C O L U M N

FIGIJRE . TEVPERTURE GR ~ D I E U THROUGH COLUMUThis process may sound involved, but aboye the feedplate the penta ne an d heavier usually fade out of th e pictureso quickly tha t the est imation is reasonably rapid. At any

rate, i t is far shor ter and more sat isfactory than the moreobvious me tho d of estimating overhead and botto m con-centrations of th e materials present in traces only and check-ing them by refiguring th e whole column.I n computing the ethane, it is desirable to express theamo unt on th e feed plate to a precision far beyond th atwith which it can possibly be known, a precision unjusti-f ied, for example, by the uncer tainty in the extrapolatedvalue of P z which is us3d in determining it. Th e reasonfor this is th e extreme sensitiveness of t he larger an d impor-tant concentrat ions on th e plates above to very minor changesin this value of the Concentration on the feed plate.DISCLSSIOSF REsuLw

The concentrat ions and temperatures thus computed areplotted in Figures 1 and 2. The abscissas are plate num-bers indicated by subscripts 1, 2, etc. Where the pointwas computed f rom the botto m of th e column, the abscissasare given a t the bo ttom of the figures; where computedf ro m t h e t o p t h e p l a te n u m b ers a r e s h o m a t t h e t o p of t h ediagram. It will be noted th at these abscissas do not corre-spond exactly . Th e concentrations working u p meet thecurve working down in between plates . This means thatthe column balance is not such that an integral number oftheoretically perfect plates will function in this way. How-ever, as in the case of design of column s for bina ry mixtu res,using the next largest number of integral plates will givea column which will give a somewhat hetter separat ion.In this case, as in the ordinary one, i t is unnecessary t o tryto r ead jus t top and bo t tom condi t ions so tha t the p la tenumbers come ou t exactly integral .

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49 8 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 24, NO.,^It is worthy of note that the temperature gradient ofFigure 2 is nearly uniform above and below the feed plate.This is quite different from the corresponding plot of abinary mixture, where the temperature gradient is largenear the feed plate and small toward both ends of th e column.This difference is due to the fact that, in complex hydro-carbon mixtures of several components, the components

of intermediate boiling point accumulate in the middle ofthe column in a way th at effectively flattens out th e tempera-ture curve.It should be clear that the low-temperature portion ofthe curves is calculated down from the t op of th e column,and the high-temperature part up from the bot tom. Thesetwo portions blend in tangentially where they meet. How-ever, if the upper port ions are cont inued down, they givea too low value of temperature and a too high value of th elow-boiling constituents, because in calculating downwardfrom the top it is impossible to allow for the high-boilingconstituents. This portion of the curve is shown dottedin Figure 1.The only point regarding the concentration curve whichmerits special attentio n is the accumu lation of butan e inthe middle par t of the column. This is the component ofboiling point intermediate between the bottom and top tem-peratures of the column, and, as already indicated, this ac-cumulation in the middle of the column is characteristic.The slight rise in butane concentration on the first plate abovethe feed is more striking. While the general tren d of buta neconcentration above the feed plate is downward, a rise ofthis sort may occur where the temperature is sufficientlyhigh to give a value of P , sufficient to reverse the slope ofthe Hausbran d l ine.Dependable data as to plate efficiency in natural gaso-line columns are exceedingly meager, b ut all the indication sare tha t the efficiencies are high. Th us, a sample of th eliquid on the plate in the upp er pa rt of a column gave uponanalysis 15.7 mole per cent propane and 70 mole per cent

butane. Using Raoults law, the vapor in equilibrium withthis liquid should contain 47 per cent propane and 49.3 percent butane. A sample of the vapor rising from this plateshowed upon analysis 49.3 per cent propane and 53.8 percent butane. In other words, the vapor rising from theplate was r icher in butane and poorer in propane than i twould have been had it left the plate in equilibrium withthe liquid on it . This is anoth er way of saying that th eliquid on the plate had not completely dissolved the butaneou t of the vapor rising into the plate, down to the equilib-rium value. However, the difference in com position issmall. Th e vapor approache d closely to equilibrium withthe liquid, which means t ha t th e plate efficiency was reason-ably high. It is very desirable that accurate determinationsof ac tua l plate efficiency an d of th e heigh t of th e equivalenttheoretical plate for the different types of tower-filling usedin the industry be mad e in order to serve as a sui table guidefo r designing and operating engineers.

SUhlM.4RYThe Hausbrand equat ion for the calculat ion of plate-to-plate concentration gradients in the rectification of binary

mixtures can be applied directly to the calculation of gradientsin the isopiestic rectification of mixtures however com-pIex, provided the composition of the feed and the point andsharpness of cu t be known, an d the co mpo nents of th e mix-ture follow Raoults law. These equations are, therefore,direc tly applicable in the design of rectification equ ipm entfo r natural or refinery gasolines and, in general, for anymixture of hydrocarbons in which the concentrat ions ofthe individual components are known.LITERATURE ITED

(1) McAdams, W. H., and Morrell. J. C. I N D ENO (HEX.. 6. .